CUDA is a GPU programming environment developed by Nvidia.
There are actually two languages in question: one for building code to run on the GPU, and one for building code to run on the CPU. Neither are standard C or standard C++; both are a subset of standard C++. Neither is a superset of C, but code written in this language strongly resembles what is normally called "C-style" code, i.e. C++ code which mostly uses features from the common subset of C and C++.
Confusingly, Nvidia market the languages as "Cuda C" despite the fact that they are C++ with some features removed. Nvidia say that they are working to gradually increase the amount of standard C++ which is supported.